Problem: In Takahashi's mind, there is always an integer sequence of length 2 \times 10^9 + 1: A = (A_{-10^9}, A_{-10^9 + 1}, ..., A_{10^9 - 1}, A_{10^9}) and an integer P.

Initially, all the elements in the sequence A in Takahashi's mind are 0, and the value of the integer P is 0.

When Takahashi eats symbols `+`, `-`, `>` and `<`, the sequence A and the integer P will change as follows:

* When he eats `+`, the value of A_P increases by 1;
* When he eats `-`, the value of A_P decreases by 1;
* When he eats `>`, the value of P increases by 1;
* When he eats `<`, the value of P decreases by 1.



Takahashi has a string S of length N. Each character in S is one of the symbols `+`, `-`, `>` and `<`. He chose a pair of integers (i, j) such that 1 \leq i \leq j \leq N and ate the symbols that are the i-th, (i+1)-th, ..., j-th characters in S, in this order. We heard that, after he finished eating, the sequence A became the same as if he had eaten all the symbols in S from first to last. How many such possible pairs (i, j) are there?

Constraints

* 1 \leq N \leq 250000
* |S| = N
* Each character in S is `+`, `-`, `>` or `<`.

Input

Input is given from Standard Input in the following format:


N
S


Output

Print the answer.

Examples

Input

5
+>+<-


Output

3


Input

5
+>+-<


Output

5


Input

48
-+><<><><><>>>+-<<>->>><<><<-+<>><+<<>+><-+->><<


Output

475

Solution (in CPP):

Solution:
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<map>
#define ll long long
#define MN 250005
using namespace std;
inline ll in(){
    ll x=0;bool f=0;char c;
    for (;(c=getchar())<'0'||c>'9';f=c=='-');
    for (x=c-'0';(c=getchar())>='0'&&c<='9';x=(x<<3)+(x<<1)+c-'0');
    return f?-x:x;
}
map <ll,int> mp;
const ll mod=4172596182543704117ll;
const ll Mod=233;
ll h[MN];
ll n,x,y,sum,bt,res,tmp;
char s[MN];
inline ll qmul(ll x,ll y){
	ll res=0;
	while (y){
		if (y&1) res=(res+x)%mod;
		x=(x+x)%mod;y>>=1; 
	}return res;
}
inline ll qpow(ll x,ll y){
	ll res=1;
	while (y){
		if (y&1) res=qmul(res,x)%mod;
		x=qmul(x,x)%mod;y>>=1;
	}return res;
}
int main()
{
	n=in();scanf("%s",s);
	bt=1;x=Mod;y=qpow(x,mod-2);
	for (int i=1;i<=n;++i){
		h[i]=h[i-1];
		if (s[i-1]=='+') h[i]=(h[i]+bt)%mod;
		else if (s[i-1]=='-') h[i]=(h[i]+mod-bt)%mod;
		else if (s[i-1]=='<') bt=qmul(bt,x);
		else if (s[i-1]=='>') bt=qmul(bt,y);
		++mp[h[i]];
	}bt=1;
	for (int i=1;i<=n;++i){
		tmp=qmul(h[n],bt);tmp=(tmp+sum)%mod;
		res+=mp[tmp];
		if (s[i-1]=='+') sum=(sum+bt)%mod;
		else if (s[i-1]=='-') sum=(sum+mod-bt)%mod;
		else if (s[i-1]=='<') bt=qmul(bt,x);
		else if (s[i-1]=='>') bt=qmul(bt,y);
		--mp[h[i]];
	}printf("%lld",res);return 0;
}